This document contains the full B.Tech (Semester IV) Theory Examination 2024–25 question paper for Signal System (BEC403). The paper spans two printed pages, carries 70 marks, and evaluates a student's understanding of continuous-time and discrete-time signals, system properties, LTI system analysis, Fourier and Laplace transforms, Z-transform concepts, sampling, convolution, and stability of systems.
Section A – Short Conceptual Questions (14 Marks)
Section A presents seven 2-mark questions, covering core signal and system principles:
Definition and examples of energy and power signals (Page 1)
Key properties of linear systems
Meaning and role of convolution in LTI system analysis
Comparison of Fourier Series vs Fourier Transform
Definition of Region of Convergence (ROC) in Z-transform
Explanation of aliasing in sampling
Concept of eigenfunctions of LSI systems
These questions validate conceptual clarity in the basics of signal processing.
Section B – Analytical & Medium-Difficulty Problems (21 Marks)
Students answer any three of five questions. Topics include:
Even & Odd Signal Decomposition
Finding even and odd parts of
x(t) = cos(t) + sin(t) + cos(t)·sin(t)
Impulse Response of LTI System
Solving differential equation
dy/dt + 2y(t) = x(t)
Convolution via Fourier Transform
Convolving:
x₁(t) = e⁻⁴ᵗ u(t)
x₂(t) = e⁻⁸ᵗ u(t)
Time-Shifting & Frequency-Shifting in Z-Transform
Derivation + examples (Page 1)
Signal Reconstruction
Explanation of interpolation technique for reconstructing signals from samples
These questions check analytical skills and mathematical application.
Section C – Long, Higher-Order Problems (35 Marks)
Section C contains five questions (Q3–Q7), each with two choices, requiring deeper understanding.
Q3 – System Testing / Signal Classification
Testing linearity, time-invariance, and causality of:
y(t) = t · x(t)
OR determining whether x(t) = e⁻⁵ᵗu(t) is an energy or power signal (Page 1)
Q4 – Convolution Integral / Stability Analysis
Compute convolution of e⁻³ᵗu(t) with u(t)
OR find step response of h(t) = e⁻⁶ᵗu(t) and check BIBO stability (Page 2)
Q5 – Inverse Laplace / DTFT Analysis
Inverse Laplace of
X(s) = 2 / ((s+4)(s−1)) with ROC: −4 < Re(s) < 1
OR DTFT of
x(n) = 0.5ⁿu(n) + 2⁻ⁿu(−n−1)
Q6 – Z-transform & ROC / Inverse Z-transform
Z-transform of sin(ω₀n)u(n) with ROC
OR inverse Z-transform of
H(z) = 0.2z / [(z + 0.4)(z − 0.2)] with ROC: |z| > 0.4
Q7 – Sampling Theorem / Aliasing
Statement & proof of Sampling Theorem and effect of undersampling
OR determining aliasing for
x(t) = cos(500πt) + sin(700πt)
sampled at 400 Hz
These questions test deep conceptual knowledge, mathematical handling, and system behavior analysis.
Summary
The Signal System (BEC403) exam paper comprehensively evaluates:
Continuous & discrete signals
Energy vs power classification
LTI systems & convolution
Fourier Transform & Fourier Series
Z-transform & Laplace transform
Sampling theorem & aliasing
Stability, causality, linearity & time-invariance
DTFT and inverse Z-transform concepts
System responses (impulse & step)
This is a complete academic resource for students studying the fundamentals of signal and system analysis in electronics and communication engineering.
